Large-scale election campaigns: Combinatorial Shift Bribery

Robert Bredereck, Piotr Faliszewski, Rolf Niedermeier, Nimrod Talmon

Research output: Contribution to journalReview articlepeer-review

28 Scopus citations


We study the complexity of a combinatorial variant of the Shift Bribery problem in elections. In the standard Shift Bribery problem, we are given an election where each voter has a preference order over the set of candidates and where an outside agent, the briber, can pay each voter to rank the briber's favorite candidate a given number of positions higher. The goal is to ensure the victory of the briber's preferred candidate. The combinatorial variant of the problem, introduced in this paper, models settings where it is possible to affect the position of the preferred candidate in multiple votes, either positively or negatively, with a single bribery action. This variant of the problem is particularly interesting in the context of large-scale campaign management problems (which, from the technical side, are modeled as bribery problems). We show that, in general, the combinatorial variant of the problem is highly intractable; specifically, NP-hard, hard in the parameterized sense, and hard to approximate. Nevertheless, we provide parameterized algorithms and approximation algorithms for natural restricted cases.

Original languageEnglish
Pages (from-to)603-652
Number of pages50
JournalJournal Of Artificial Intelligence Research
StatePublished - 1 Mar 2016
Externally publishedYes

ASJC Scopus subject areas

  • Artificial Intelligence


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